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Using our optimization methods, find two positive numbers, x and y, such that 3x + 12y is a maximum given that their product, xy, is

Using our optimization methods, find two positive numbers, x and y, such that 3x + 12y is a maximum given that their product, xy, is 144 and x lies in the interval [10, 50]. Be sure to give both x and y. Provide justification for your answer.

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